The necessary condition and sufficient conditions for wavelet frame on local fields

In the paper entitled “Multiresolution analysis on local fields” [H.K. Jiang, D.F. Li, N. Jin, Multiresolution analysis on local fields, J. Math. Anal. Appl. 294 (2) (2004) 523–532], we establish the orthonormal wavelet construction from multiresolution analysis on local fields. The objective of this paper is to construct wavelet frame on local fields. A necessary condition and four sufficient conditions for wavelet frame on local fields are given. An example is presented at the end.